21. 22. 23. 24. 25. Classify and reduce the second order partial differential equation Uxx - 4xllyy = 1 x -ux into canonical form and hence, find the general solution. 1 3 a+2h Derive Simpson's rd rule to evaluate the integral ( f(x)dx. Estimate the error. Find the eigenvalues and the eigenfunctions of the functional J(y)=(y + y)dx subject to the conditions y(0) =y(1)=0, ydx=1. Find the resolvent kernel for the integral equation o(s) = f(s)+(st+st)(t)dt -1 Show that the transformation 0 2q Q=tan P = q + p 1 is canonical. Find a generating function. 4 P